1. Advances in Robustness Assessment for Multi-storey Steel-framed Buildings
Bassam A. Izzuddin
Computational Structural Mechanics Group
Department of Civil and Environmental Engineering
Imperial College London
The 11th Pacific Structural Steel Conference
Shanghai, October 2016

2. Overview Introduction Robustness limit state for sudden column loss
Multi-level robustness assessment framework
Nonlinear static response
Simplified dynamic assessment
Ductility limit
Significance of modelling assumptions
Realistic modelling of composite floor
Contribution of infill panels
Influence of steel rate-sensitivity
Conclusions

3. Introduction Disproportionate collapse WTC (2001) Ronan Point (1968)
Structures cannot be designed to withstand unpredictable extreme events
But they should be designed for structural robustness:
the ability of the structure to withstand the action of extreme events without being damaged to an extent disproportionate to the original cause
WTC (2001)
Setúbal, Portugal (2007)
Ronan Point (1968)
Disproportionate: No
Robust structure
Disproportionate: Yes

4. Introduction Robustness design
Prescriptive approach after Ronan Point (1968)
Tying provisions irrational with neglect of ductility, and largely inadequate even if beneficial
Not permitted for Class 3 (high-rise) buildings
Need for a performance-based design approach
Large deformations under rare extreme events
Design envelope stretched beyond strength limit to ductility limit
Quantification of safety margin
Emergence of robustness assessment for sudden column loss
USA codes: GSA (2003), UFC (2009)
Multi-level framework developed at Imperial College

5. Robustness limit state for sudden column loss
Sudden column loss (SCL)
Event-independent scenario
Robustness limit state
Prevention of upper floor collapse
Allow large deformations
Within ductility limit
More than just a standard test of robustness
SCL vs column damage by blast
Comparison of deformation demands in upper floors
SCL presents an upper bound on floor deformations
SCL can be assessed without full nonlinear dynamic analysis
Sudden
column loss

6. Multi-level robustness assessment framework
Robustness limit state
Prevention of collapse of upper floors
Ductility: demand  supply
Two stages of assessment
Nonlinear static response accounting for ductility limit
Simplified dynamic assessment

7. Multi-level robustness assessment framework
Maximum gravity load sustained under sudden column loss
Applicable at various levels of structural idealisation
Simplified assembly of lower into higher level response
For specific level of idealisation require
Nonlinear static response
Simplified dynamic assessment
Ductility limit
Planar effects are neglected
Floors identical in components and loading
Reduced model where deformation is concentrated
Columns can resist re-distributed load

8. Multi-level robustness assessment framework Nonlinear static response
Sudden column loss similar to sudden application of gravity load to structure without column
Maximum dynamic response can be approximated using amplified static loading (ld P)
Need models beyond conventional strength limit, including hardening, tensile catenary and compressive arching actions
DIF

9. Multi-level robustness assessment framework Simplified dynamic assessment
Based on conservation of energy
Work done by suddenly applied load equal to internal energy stored
Leads to maximum dynamic displacement (also to DIF)
Definition of “pseudo-static” response
DIF = (ld/l) << 2

10. Multi-level robustness assessment framework Ductility limit
Typically based on based on failure of connection components
Rotational and axial deformations
Ductility limit based on first component failure is conservative
Successive component failures can be easily considered
Dominant deformation mode
No need to define ductility limit in terms of a specific drop in static resistance

11. Multi-level robustness assessment framework Ductility limit
Flooring system subject to initial sudden column loss followed by a first component failure, then full system failure
Maximum pseudo-static capacity may not even be related to a specific ductility limit
…but not with more severe first component failure
…unless system ductility and static resistance picks up
Maximum load at intersection between pseudo-static and descending static curves
… for instance following a compressive arching stage
Residual pseudo-static capacity after first component failure
Static response of initially damaged structure
First component failure
Complete system failure
Static response of undamaged structure

12. Multi-level robustness assessment framework Ductility limit
UFC code allows nonlinear static analysis, with DIF defined in terms of ductility limit
Consistent with elastic-plastic response
Can be grossly incorrect and unsafe with catenary or compressive arching action
Pseudo-static energy balance approach
Rational application with nonlinear static analysis
Avoids demanding nonlinear dynamic analysis
‘Pseudo-static capacity’ as a rational performance-based measure of structural robustness
Combines redundancy, ductility and energy absorption within a simplified framework

13. Significance of modelling assumption
transverse primary beam
Edge beam connections
Gravity load = 1.0 DL+0.25 IL
internal secondary beams
Grillage approximation:
7-storey steel framed composite building with simple frame design
Sudden loss of peripheral column
Assuming identical floors  assessment at floor level of idealisation
edge beam

14. Significance of modelling assumption
Pseudo-static response of individual beams
Simplified assembly to obtain pseudo-static capacity of floor slab
Importance of connection ductility, additional reinforcement and axial restraint
Inadequacy of prescriptive tying force requirements

15. Significance of modelling assumption
Pseudo-static response curves of edge beam
Pseudo-static response curves of internal beams
Pseudo-static response curves of transverse beam

16. Significance of modelling assumption
Assumed deformation mode defines ductility limit
Case 2 (r=2% with axial restraint) is just about adequate
Inadequacy of prescriptive tying force requirements φj
δSB3
δSB1
δSB2
δMB
ρmin, EC4,
w/ axial restraint
ρ = 2%,
w/ axial restraint
ρ = 2%,
w/ο axial restraint
Bare-steel frame,
w/ axial restraint

17. Significance of modelling assumption Realistic modelling of composite floor
Pseudo-Static Capacity
(kN)
Maximum Deflection
(mm)
Capacity/Demand Ratio
Simplified Grillage(*)
846
392.3
1.135
Detailed Grillage
1057
359.5
1.420
Composite Floor
1166
356.9
1.564
+25%
+38%

18. Significance of modelling assumption Contribution of infill panels
Pseudo-static response of individual infill panels
May be assembled at different levels of structural idealisation
May be considered at single floor level, subject to regularity, but should be scaled
Number of floors above removed column

19. Significance of modelling assumption Contribution of infill panels
Modelling of infill panels
Simplified strut models
Advanced mesoscale NLFE models
16-Noded Interface FE
Struts Representing Infill Walls
20-Noded Solid FE
Structural Frame Elements
Full 3D Model

20. Significance of modelling assumption Contribution of infill panels
Significant enhancement of pseudo-static capacity, particularly for lower column loss
For solid/perforated panels, with/without gaps
Pseudo-static capacity achieved at relatively small displacements of 10-15mm

21. Significance of modelling assumption Influence of steel rate-sensitivity
Instantaneous column loss
Subsequent dynamic floor deformation
Typical duration of ~0.5s from rest to maximum displacement
Strain-rate ~0.3s-1 in critical steel components
Potential increase in dynamic yield strength between 10-50%

22. Significance of modelling assumption Influence of steel rate-sensitivity
Collaborative experimental programme with University of Trento
Coupon and T-stub tests on mild steel specimens
Deformation rates representative of robustness limit state
Enhancement of material yield and ultimate strength 6-15%
Enhancement of T-stub resistance 2-10%
Influence rate-sensitivity on overall pseudo-static capacity, hence robustness, is insignificant
~125 mm/s
~0 mm/s
~0 s-1
~0.3 s-1
~2.0 s-1

23. Conclusions Simplified robustness assessment framework
Multi-storey buildings subject to sudden column loss
Multi-level framework utilising nonlinear static response
Simplified dynamic assessment using energy balance
Pseudo-static capacity as rational measure of robustness
Inadequacy of DIF approach in UFC
Significance of modelling assumptions
Modelling composite slab with 2D shell elements can enhance pseudo-static capacity by ~40% compared to grillage models
Masonry infill can enhance pseudo-static capacity by ~60%-500% depending on openings, gaps and number of floors above
Steel rate-sensitivity has a negligible influence on robustness under sudden column loss

24. Advances in Robustness Assessment for Multi-storey Steel-framed Buildings
Bassam A. Izzuddin
Computational Structural Mechanics Group
Department of Civil and Environmental Engineering
Imperial College London
The 11th Pacific Structural Steel Conference
Shanghai, October 2016